Large Torsional Oscillations in Suspension Bridges Revisited: Fixing an Old Approximation

Summary: This paper explores the possibility that if one is interested in a simple version of the Tacoma Narrows Bridge mystery, namely large amplitudinal torsional oscillation about an equilibrium, then the puzzle might have its roots in a simple trigonometric approximation introduced in the engineering literature in 1950.

About the Author: (from The American Mathematical Monthly, vol. 106, (1999)) P. J. McKenna did his undergraduate work in Dublin (at U.C.D.) and his graduate work in Ann Arbor. The central theme of his research is nonlinear analysis, in particular, the existence, multiplicity, and numerical approximation of solutions of nonlinear boundary value problems. The work arises naturally from his research in multiple periodic solution of Hamiltonian systems. Kristen Moore, his doctoral student, is extending this analysis to the partial differential equations that describe the spatial behavior along the length of the bridge.